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3 years ago

System of equations- does this have one solution, many solutions or no solution

Mathematics

1 answer:

Alla [95]3 years ago

3 0

Answer:

One solution

Step-by-step explanation:

Let's rewrite y = 6 - 3x as y = -3x + 6

Looking at these two equations, we can see they share a y-intercept

Making our solution 6

We know there is only one solution because the equations are not the exact same, if they were we'd have infinitely many solutions

We also know there aren't no solutions because the lines are not parallel (same slopes with difference y-intercepts)

Best of luck

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Indicate the equation of the given line in standard form.

Lorico [155]

We have that
triangle ABC
where
A(-5, 5), B(1, 1), and C(3, 4) are the vertices

using a graph tool
see the attached figure

the hypotenuse is the segment AC

find the equation of the line AC
A(-5, 5) C(3, 4)

step 1
find the slope m
m=(y2-y1)/(x2-x1)-----> m=(4-5)/(3+5)-----> m=-1/8

step 2
with C(3,4) and m=-1/8
find the equation of a line
y-y1=m*(x-x1)-----> y-4=(-1/8)*(x-3)----> y=(-1/8)*x+(3/8)+4
y=(-1/8)*x+(3/8)+4----> multiply by 8----> 8y=-x+3+32
8y=-x+35
the standard form is Ax+By=C
so
x+8y=35
A=1
B=8
C=35

the answer is
x+8y=35

7 0

3 years ago

The formula for the slant height of a cone is , where S is surface area of the cone. Use the formula to find the slant height, l

liq [111]

we know that

The formula of the surface area of the cone is equal to

$SA=\pi r^{2}+\pi rl$

where

SA is the surface area

r is the radius of the cone

l is the slant height

in this problem we have

$SA=500\pi\ ft^{2}\\r=15\ ft\\l=?$

Solve the formula for l

$SA=\pi r^{2}+\pi rl\\ \\\pi rl=SA-\pi r^{2} \\ \\l=\frac{SA-\pi r^{2} }{\pi r}$

substitute the values

$l=\frac{500\pi -\pi 15^{2} }{\pi15}\\ \\l=\frac{275}{15}\ ft\\ \\l=\frac{55}{3}\ ft\\ \\l=18\frac{1}{3}\ ft$

therefore

the answer is

The slant height is $18\frac{1}{3}\ ft$

7 0

3 years ago

Read 2 more answers

What is the correct slope intercept form of the equation y + 16 = 3(x - 0) ?

Sindrei [870]

slope intercept form is just solve for y

y+16=3(x-0)

y+16=3(x)

y+16=3x

mius 16 both sides

y=3x-16

3rd option

8 0

3 years ago

Whats the answer & how do I solve it ?

Veseljchak [2.6K]

Answer:

Area of rectangle = 225/2 or 112.5

Step-by-step explanation:

Given,

Consider a rectangle ABCD.

Let AC be a diagonal of rectangle of length = 15

In triangle ABC.

Sin 45° =height/hypotenuse {SinФ = height / hypotenuse}

Here, hypotenuse = diagonal of rectangle ( i.e AC = 15)

And height is AB

Therefore, sin 45° = AB/AC

or sin 45° = AB / 15

or 1/√2 = AB /15

AB = 15/√2

Similarly we can find Base (i.e BC) using cosine.

Cos 45° = Base/Hypotenuse

Cos 45° = BC / AC

or 1/√2 = BC/15

BC = 15/√2

Hence we got length of rectangle , AB= 15/√2

And width of rectangle , BC = 15/√2

Therefore, area of rectangle = Length × Width

Area of rectangle = 15/√2 × 15/√2 = 225/2

Hence, area of rectangle = 225/2 = 112.5

6 0

3 years ago

Simplify x^6+10x^5+25x^4-x^2-10x-25 using synthetic division

antiseptic1488 [7]

Saan po yung divisor?

Kailangan ko po

7 0

2 years ago